A control device of a vehicle drive device executing a fuel cut interrupting fuel supply to an engine is well known in the vehicle drive device including an electric motor coupled in a power transmitting path between the engine and drive wheels. For example, this corresponds to an engine start control device described in Patent Document 1. If the engine is started by the electric motor, the engine start control device of Patent Document 1 stops a fuel cut for the engine and starts the engine at the same time when an accelerator pedal is depressed after a brake is released.